Extracting method of pattern contour, image processing method, searching method of pattern edge, scanning method of probe, manufacturing method of semiconductor device, pattern inspection apparatus, and program

ABSTRACT

An extracting method of a pattern contour, includes acquiring an image of a pattern to be inspected, calculating a schematic edge position of the pattern from the image, preparing an approximate polygon by approximating a polygon consisting of edges having predetermined direction components to a contour shape of the pattern on the basis of the calculated edge position, dividing the approximate polygon into star-shaped polygons, calculating the position of a kernel of the star-shaped polygon, and searching an edge of the pattern in a direction connecting the kernel to an arbitrary point positioned on the edge of the approximate polygon.

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims benefit of priority under 35USC §119 toJapanese patent application No. 2002-239194, filed on Aug. 20, 2002, thecontents of which are incorporated by reference herein.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to an extracting method of apattern contour, an image processing method, a searching method of apattern edge, a scanning method of a probe, a manufacturing method of asemiconductor device, a pattern inspection apparatus, and program. Thepresent invention relates to, for example, evaluation of a fine patternin a manufacturing process of the semiconductor device.

[0004] 2. Related Background Art

[0005] In a manufacturing process of a semiconductor device, an opticalmicroscope or a scanning electron microscope (hereinafter referred to asan SEM) is used to inspect a fine pattern.

[0006] In recent years, multifactorial inspection and control ofpatterns have extensively implemented with a positive use oftwo-dimensional configuration information of a pattern image outputtedfrom an inspection apparatus. Basis of this technique is a technique ofextracting a contour of the pattern from an inspection image thereofgiven by a gray scale or color distribution.

[0007] For a simply linear pattern, for example, as shown in FIG. 43, amethod has heretofore frequently been used comprising: searching an edgealong directions SD202 vertical to a longitudinal direction of a linearpattern PT200; and analyzing gray scale data at the time to calculate anedge position based on a threshold value method.

[0008] In addition, for a pattern having a schematically convex shape,for example, a hole pattern PT210 shown in FIG. 44, there is a method ofradially searching a pattern edge as shown by searching directions SD212in the drawing. This method is described, for example, in JapanesePatent Application Laid-Open Nos. 7-27548 and 2001-91231.

[0009] However, even with the use of the above-described method, edgesof some patterns are wrongly detected, for example, as patterns shown inFIG. 45, the contour shape of which are complicated, and when the edgesare simply searched in directions SD214 extending in parallel with oneanother. Since an image Img2 in FIG. 45 includes a plurality of patternsPT2, PT4, PT6, the detected edges have to be attributed to any of thepatterns, respectively. For this, an operator needs to designate aregion where the pattern exists prior to the search of the patterns.Alternatively, the method has to comprise: performing image matchingwith design data to automatically attribute the edge; or again groupingextracted edge point sequence data. Any arrangement requires complicatedprocessing, inspection efficiency has thus not been satisfactory.

[0010] Furthermore, when a plurality of patterns similar to one anotherexist in the image, it is frequently necessary to automatically andselectively designate a specific pattern from the plurality of patternsand to inspect the pattern. In this case, the method described, forexample, in Japanese Patent Application Laid-Open No. 2001-148016 can beused, but it is difficult to apply this method to cases other than acase in which the plurality of patterns are regularly arranged. Sincethe matching is performed by calculation of correlation among gray scaleimage data, a long processing time has been required.

[0011] There have been proposed a large number of methods of preferablydetecting a pattern edge for patterns having complicated contours. Inthe searching of the pattern edge, it is desirable to set the edgesearching direction to a direction substantially orthogonal to thepattern edge in order to enhance solution of the edge position,

[0012] However, even when an edge of a polygon PLG2 shown in FIG. 46 isset as a schematic pattern edge for a pattern PT44 shown in the figure,and as long as the edge is searched in a direction along a straightline, the edge is searched in a direction similar to that of the edge asshown by searching directions SD216 c, SD216 d. In this manner, it issometimes difficult to search the edges in directions crossing at rightangles to all the pattern edges.

BRIEF SUMMARY OF THE INVENTION

[0013] According to a first aspect of the invention, there is providedan extracting method of a pattern contour, comprising:

[0014] acquiring an image of a pattern to be inspected;

[0015] calculating a schematic edge position of the pattern from theimage;

[0016] preparing an approximate polygon by approximating a polygonconsisting of edges having predetermined direction components to acontour shape of the pattern on the basis of the calculated edgeposition;

[0017] dividing the approximate polygon into star-shaped polygons;

[0018] calculating the position of a kernel of the star-shaped polygon;and

[0019] searching an edge of the pattern in a direction connecting thekernel to an arbitrary point positioned on the edge of the approximatepolygon.

[0020] According to a second aspect of the invention, there is providedan extracting method of a pattern contour, comprising:

[0021] acquiring an image of a pattern to be inspected;

[0022] calculating a schematic edge position of the pattern from theimage;

[0023] generating a lattice whose unit cell has a size larger than thatof a pixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;

[0024] applying a lattice animal onto the lattice based on the weightcoefficient; and

[0025] outputting contour data of the pattern based on coordinate dataof a vertex of the applied lattice animal.

[0026] According to a third aspect of the invention, there is provided aprogram which allows a computer to implement an extracting method of apattern contour, comprising:

[0027] acquiring an image of a pattern to be inspected;

[0028] calculating a schematic edge position of the pattern from theimage;

[0029] preparing an approximate polygon by approximating a polygonconsisting of edges having predetermined direction components to acontour shape of the pattern on the basis of the calculated edgeposition;

[0030] dividing the approximate polygon into star-shaped polygons;

[0031] calculating the position of a kernel of the star-shaped polygon;and

[0032] searching an edge of the pattern in a direction connecting thekernel to an arbitrary point positioned on the edge of the approximatepolygon.

[0033] According to a fourth aspect of the invention, there is provideda program which allows a computer to implement an extracting method of apattern contour, comprising:

[0034] acquiring an image of a pattern to be inspected;

[0035] calculating a schematic edge position of the pattern from theimage;

[0036] generating a lattice whose unit cell has a size larger than thatof a pixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;

[0037] applying a lattice animal onto the lattice based on the weightcoefficient; and

[0038] outputting contour data of the pattern based on coordinate dataof a vertex of the applied lattice animal.

[0039] According to a fifth aspect of the invention, there is provided amanufacturing method of a semiconductor device, comprising an extractingmethod of a pattern contour, the extracting method comprising:

[0040] acquiring an image of a pattern to be inspected;

[0041] calculating a schematic edge position of the pattern from theimage;

[0042] preparing an approximate polygon by approximating a polygonconsisting of edges having predetermined direction components to acontour shape of the pattern on the basis of the calculated edgeposition;

[0043] dividing the approximate polygon into star-shaped polygons;

[0044] calculating the position of a kernel of the star-shaped polygon;and

[0045] searching an edge of the pattern in a direction connecting thekernel to an arbitrary point positioned on the edge of the approximatepolygon.

[0046] According to a sixth aspect of the invention, there is provided amanufacturing method of a semiconductor device, comprising an extractingmethod of a pattern contour, the extracting method comprising:

[0047] acquiring an image of a pattern to be inspected;

[0048] calculating a schematic edge position of the pattern from theimage;

[0049] generating a lattice whose unit cell has a size larger than thatof a pixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;

[0050] applying a lattice animal onto the lattice based on the weightcoefficient; and

[0051] outputting contour data of the pattern based on coordinate dataof a vertex of the applied lattice animal.

[0052] According to a seventh aspect of the invention, there is providedan image processing method comprising:

[0053] acquiring an image of a pattern to be inspected;

[0054] extracting a part of a point sequence which belongs to a contourof the pattern;

[0055] preparing a Voronoi diagram with respect to the extracted partialpoint sequence;

[0056] searching a point which belongs to an edge of the pattern alongan edge of the prepared Voronoi diagram to incorporate the searchedpoint into the partial point sequence; and

[0057] removing the edge of the Voronoi diagram intersecting with thecontour of the pattern to define a sub-region in the image.

[0058] According to an eighth aspect of the invention, there is provideda program which allows a computer to implement an image processingmethod comprising:

[0059] acquiring an image of a pattern to be inspected;

[0060] extracting a part of a point sequence which belongs to a contourof the pattern;

[0061] preparing a Voronoi diagram with respect to the extracted partialpoint sequence;

[0062] searching a point which belongs to an edge of the pattern alongan edge of the prepared Voronoi diagram to incorporate the searchedpoint into the partial point sequence; and

[0063] removing the edge of the Voronoi diagram intersecting with thecontour of the pattern to define a sub-region in the image.

[0064] According to a ninth aspect of the invention, there is provided amanufacturing method of a semiconductor device, comprising an imageprocessing method including:

[0065] acquiring an image of a pattern to be inspected;

[0066] extracting a part of a point sequence which belongs to a contourof the pattern;

[0067] preparing a Voronoi diagram with respect to the extracted partialpoint sequence;

[0068] searching a point which belongs to an edge of the pattern alongan edge of the prepared Voronoi diagram to incorporate the searchedpoint into the partial point sequence; and

[0069] removing the edge of the Voronoi diagram intersecting with thecontour of the pattern to define a sub-region in the image.

[0070] According to a tenth aspect of the invention, there is provided asearching method of a pattern edge, comprising:

[0071] acquiring an image of a pattern to be inspected and data of aline representing a schematic edge position of the pattern;

[0072] defining one arbitrary point in the image as a start point ofedge searching, and defining at least one point on the line as a pointin an edge searching direction; and

[0073] searching the edge of the pattern from the start point of theedge searching and along at least one curve of a curve group given byeither a real part or an imaginary part of a holomorphic function, atrajectory of the curve passing through the point in the edge searchingdirection.

[0074] According to an eleventh aspect of the invention, there isprovided a program which allows a computer to implement a searchingmethod of a pattern edge, the searching method comprising:

[0075] acquiring an image of a pattern to be inspected and data of aline representing a schematic edge position of the pattern;

[0076] defining one arbitrary point in the image as a start point ofedge searching, and defining at least one point on the line as a pointin an edge searching direction; and

[0077] searching the edge of the pattern from the start point of theedge searching and along at least one curve of a curve group given byeither a real part or an imaginary part of a holomorphic function, atrajectory of the curve passing through the point in the edge searchingdirection.

[0078] According to a twelfth aspect of the invention, there is provideda manufacturing method of a semiconductor device, comprising a searchingmethod of a pattern edge, the searching method including:

[0079] acquiring an image of a pattern to be inspected and data of aline representing a schematic edge position of the pattern;

[0080] defining one arbitrary point in the image as a start point ofedge searching, and defining at least one point on the line as a pointin an edge searching direction; and

[0081] searching the edge of the pattern from the start point of theedge searching and along at least one curve of a curve group given byeither a real part or an imaginary part of a holomorphic function, atrajectory of the curve passing through the point in the edge searchingdirection.

[0082] According to a thirteenth aspect of the invention, there isprovided a method of scanning a probe onto at least a part of anobservation region including a pattern to be inspected, comprising:

[0083] defining one arbitrary point in the observation region as a startpoint of probe scanning, and defining at least one point on a linerepresenting the schematic edge position of the pattern as a point in aprobe scanning direction; and

[0084] scanning the probe from the start point of the probe scanning andalong at least one curve of a curve group given by either a real part oran imaginary part of a holomorphic function, a trajectory of thescanning passes through a point in the probe scanning direction.

[0085] According to a fourteenth aspect of the invention, there isprovided a program to allow a computer to implement a method of scanninga probe onto a sample having an observation region, the computercontrolling an inspection apparatus to generate the probe and to scanthe probe onto at least a part of the observation region in which thepattern to be inspected is formed, the scanning method comprising:

[0086] defining one arbitrary point in the observation region as a startpoint of probe scanning, and defining at least one point on a linerepresenting a schematic edge position of the pattern as a point in aprobe scanning direction; and

[0087] scanning the probe from the start point of the probe scanning andalong at least one curve of a curve group given by either a real part oran imaginary part of a holomorphic function, a trajectory of thescanning passes through a point in the probe scanning direction.

[0088] According to a fifteenth aspect of the invention, there isprovided a manufacturing method of a semiconductor device, comprising amethod of scanning a probe onto at least a part of an observation regionin which a pattern to be inspected is formed, the method of scanning theprobe including:

[0089] defining one arbitrary point in the observation region as a startpoint of probe scanning, and defining at least one point on a linerepresenting a schematic edge position of the pattern as a point in aprobe scanning direction; and

[0090] scanning the probe from the start point of the probe scanning andalong at least one curve of a curve group given by either a real part oran imaginary part of a holomorphic function, a trajectory of thescanning passes through a point in the probe scanning direction.

[0091] According to a sixteenth aspect of the invention, there isprovided a pattern inspection apparatus comprising:

[0092] a first calculator which receives data of an image of a patternto be inspected and calculates a schematic edge position of the patternfrom the image;

[0093] an image processor which approximates a polygon constituted ofedges exclusively having predetermined direction components to a contourshape of the pattern based on the calculated edge position to prepare anapproximate polygon and which divides the approximate polygon intostar-shaped polygons;

[0094] a second calculator which calculates a position of a kernel ofthe star-shaped polygon; and

[0095] an edge searcher which searches an edge of the pattern in adirection connecting the kernel to an arbitrary point positioned on anedge of the approximate polygon.

[0096] According to a seventeenth aspect of the invention, there isprovided a pattern inspection apparatus comprising:

[0097] a calculator which receives data of an image of a pattern to beinspected and calculates a schematic edge position of the pattern fromthe image;

[0098] an image processor which generates a lattice on the image basedon the calculated edge position, a unit cell of the lattice having asize larger than that of a pixel of the image and a weight coefficientbeing allocated to each edge of the lattice, the image processorapplying a lattice animal onto the lattice based on the weightcoefficient; and

[0099] an edge searcher which outputs contour data of the pattern basedon coordinate data of a vertex of the applied lattice animal.

[0100] According to an eighteenth aspect of the invention, there isprovided a pattern inspection apparatus comprising:

[0101] a point sequence extractor which receives data of an image of apattern to be inspected and which extracts a part of a point sequencebelonging to a contour of the pattern;

[0102] an image processor which prepares a Voronoi diagram with respectto the extracted partial point sequence and which searches a pointbelonging to the edge of the pattern along an edge of the preparedVoronoi diagram to incorporate the searched point into the partial pointsequence and which removes an edge of the Voronoi diagram intersectingwith the contour of the pattern to define a sub-region in the image; and

[0103] an edge searcher which searches the edge of the pattern for eachsub-region.

[0104] According to a nineteenth aspect of the invention, there isprovided a pattern inspection apparatus comprising:

[0105] a setter which receives data of an image of a pattern to beinspected and data of a line representing a schematic edge position ofthe pattern to set a start point of edge searching and at least onepoint on the line as the point in an edge searching direction in theimage;

[0106] a calculator to calculate a curve group which is given by eithera real part or an imaginary part of a holomorphic function and each ofwhich passes through the point in the edge searching direction from thestart point; and

[0107] an edge searcher which searches an edge of the pattern along atleast one cure in the curve group.

[0108] According to a twentieth aspect of the invention, there isprovided a pattern inspection apparatus connectable to a probe scanningdevice scanning a probe onto a sample in which a pattern to be inspectedis formed, the pattern inspection apparatus comprising:

[0109] a calculator which receives image data of the pattern and data ofa line representing a schematic edge position of the pattern tocalculate a curve group given by either a real part or an imaginary partof a holomorphic function and passing through at least one point on theline representing the schematic edge position from the start point; and

[0110] a controller which generates a control signal to scan the probealong at least one curve in the curve group and which supplies thecontrol signal to the probe scanning device.

BRIEF DESCRIPTION OF THE DRAWINGS

[0111]FIG. 1 is a flowchart showing a schematic procedure of anextracting method of a pattern contour according to a first embodimentof the present invention, including an image processing method accordingto an embodiment of the present invention;

[0112]FIG. 2 is a flowchart showing procedures to arrange a latticeanimal in the flowchart of FIG. 1 in more detail;

[0113]FIG. 3 is a diagram showing one example of a pattern image;

[0114]FIG. 4A schematically shows edge data of a horizontal direction incoordinate data of a pattern edge extracted from the image shown in FIG.3, and FIG. 4B schematically shows the edge data of a vertical directionin the coordinate data of the pattern edge extracted from the imageshown in FIG. 3;

[0115]FIGS. 5A and 5B are diagrams showing results of discriminantanalysis of the coordinate data shown in FIGS. 4A and 4B;

[0116]FIG. 6 is a diagram in which horizontal components and verticalcomponents shown in FIGS. 5A and 5B are synthesized;

[0117]FIG. 7 is a diagram showing a lattice prepared in the imagecoordinate system from the judgment result shown in FIG. 6;

[0118]FIG. 8A shows one representation example of a chain code, andFIGS. 8B to 8E are diagrams showing some examples of the lattice animal;

[0119]FIG. 9 is an explanatory view of the specific procedure of themethod of disposing the lattice animal on the lattice shown in FIG. 7;

[0120]FIG. 10 is a diagram showing an optimum arrangement result of thelattice animal onto the lattice shown in FIG. 7;

[0121]FIG. 11 shows Voronoi diagram prepared with respect to vertices ofthe lattice animal shown in FIG. 10;

[0122]FIG. 12 is a diagram in which the Voronoi diagram shown in FIG. 11is synthesized;

[0123]FIG. 13 is a diagram in which a part of vertex data is removedfrom the diagram shown in FIG. 12;

[0124]FIG. 14 is a diagram showing a result of a process of dividing ananimal which exists in one sphere of influence of the diagram shown inFIG. 13 into triangles and point-coloring each vertex;

[0125]FIG. 15 is a diagram showing a result of star-shaped (convex type)polygon division of the animal arrangement obtained from the imageprocessing result shown in FIG. 14;

[0126]FIG. 16 is a diagram showing kernels of the star-shaped polygonshown in FIG. 15 and edge searching directions from these kernels;

[0127]FIG. 17 is a diagram showing one example of the image including aplurality of patterns which have schematically convex contours;

[0128]FIG. 18A shows data of edge components of a horizontal directionin the coordinate data of the pattern edge extracted from the imageshown in FIG. 17, and FIG. 18B shows the data of the edge components ofa vertical direction in the coordinate data of the pattern edgeextracted from the image shown in FIG. 17;

[0129]FIG. 19A shows a lattice generated by classifying the edgecomponents shown in FIGS. 18A and 18B, and FIG. 19B shows the animalarrangement obtained by referring to an animal table;

[0130]FIG. 20A shows a Voronoi diagram prepared with respect to thevertex of the animal shown in FIG. 19B, and FIG. 20B shows a Voronoidiagram in which Voronoi regions of FIG. 20A are integrated;

[0131]FIG. 21 is a diagram showing the edge searching directions fromthe kernels inside the animals in the regions shown in FIG. 20B;

[0132]FIG. 22A is a diagram showing one example of the lattice animalarrangement obtained from the image including a single pattern only, andFIG. 22B is a diagram showing a result of triangulation of the latticeanimal arrangement shown in FIG. 22A;

[0133]FIG. 23A shows a result of the point coloring performed withrespect to the vertices of triangles obtained in FIG. 22B, and FIG. 23Bis a diagram showing the result of kernel calculation performed withrespect to the star-shaped polygon obtained from the triangles shown inFIG. 23A;

[0134]FIG. 24 is a flowchart showing a schematic procedure of an imageprocessing method in a fourth embodiment of the present invention;

[0135]FIGS. 25A to 25D are diagrams showing specific examples of theimage processed by the procedure shown in FIG. 24;

[0136]FIGS. 26A to 26E are diagrams showing the specific examples of theimage processed by the procedure shown in FIG. 24;

[0137]FIG. 27 is a flowchart showing the schematic procedure of theimage processing method in a fifth embodiment of the present invention;

[0138]FIGS. 28A to 28D are diagrams showing the specific examples of theimage processed by the procedure shown in FIG. 27;

[0139]FIGS. 29A to 29C are diagrams showing the specific examples of theimage processed by the procedure shown in FIG. 27;

[0140]FIGS. 30A and 30B are diagrams showing the specific examples ofthe image according to a sixth embodiment of the present invention;

[0141]FIG. 31 is a flowchart showing the schematic procedure of theimage processing method in a seventh embodiment of the presentinvention;

[0142]FIGS. 32A to 32E are diagrams showing some examples of the imageprocessed by the procedure shown in FIG. 31;

[0143]FIG. 33 is a flowchart showing the schematic procedure of theimage processing method in an eighth embodiment of the presentinvention;

[0144]FIGS. 34A to 34F are explanatory views specifically showing theimage processing method shown in FIG. 33;

[0145]FIGS. 35A to 35E are explanatory views showing a method of furtherfacilitating matching of Voronoi diagrams with one another;

[0146]FIGS. 36A to 36F are explanatory views of a method ofautomatically finding a specific part from the image;

[0147]FIG. 37 is a flowchart showing the schematic procedure of an edgesearching method in a ninth embodiment of the present invention;

[0148]FIGS. 38A to 38C are diagrams showing in more detail the edgesearching method shown in FIG. 37;

[0149]FIG. 39 is a flowchart showing the schematic procedure of the edgesearching method in a tenth embodiment of the present invention;

[0150]FIGS. 40A and 40B are diagrams showing in more detail the edgesearching method shown in FIG. 39;

[0151]FIG. 41 is a flowchart showing the schematic procedure of a probescanning method and the edge searching method in an eleventh embodimentof the present invention;

[0152]FIG. 42 is a block diagram showing a schematic constitution of apattern inspection apparatus according to a twelfth embodiment of thepresent invention;

[0153]FIG. 43 is a diagram showing one example of a linear pattern andshowing an extracting method of a pattern contour according to a relatedart;

[0154]FIG. 44 is a diagram showing one example of a hole pattern andshowing the extracting method of the pattern contour according to therelated art;

[0155]FIG. 45 is a diagram showing one example of a complicated patternand showing a problem of the related art; and

[0156]FIG. 46 is an explanatory view of the problem of a pattern edgesearching method according to the related art.

DETAILED DESCRIPTION OF THE INVENTION

[0157] Embodiments of the present invention will be describedhereinafter with reference to the drawings.

[0158] In the following description, first to eighth embodiments relateto an extracting method of a pattern contour, including an imageprocessing method according to the present invention, and ninth andtenth embodiments relate to a searching method of a pattern edgeaccording to the present invention. An eleventh embodiment relates to ascanning method of a probe according to the present invention. A twelfthembodiment relates to a pattern inspection apparatus according to thepresent invention. A thirteenth embodiment relates to a manufacturingmethod of a semiconductor device according to the present invention.Furthermore, a fourteenth embodiment relates to program and computerreadable recorded medium according to the present invention. It is to benoted that in the following drawings, the same elements are denoted withthe same reference numerals, and detailed descriptions thereof areappropriately omitted.

(1) First Embodiment

[0159] A first embodiment of the present invention will be describedwith reference to FIGS. 1 to 16.

[0160]FIG. 1 is a flowchart showing a schematic procedure of theextracting method of a pattern contour according to the presentembodiment, and FIG. 2 is a flowchart showing procedures to arrange alattice animal in the flowchart of FIG. 1 in more detail.

[0161] First of all, the extracting method of the pattern contour of thepresent embodiment will schematically be described with reference to thefollowing of FIG. 1.

[0162] First, data of a gray scale image of a pattern to be inspected isacquired, for example, by an SEM (step S1). One example of the acquiredpattern image is shown in FIG. 3. An image Img2 shown in the figure isthe same as that shown in FIG. 45, and includes three patterns PT2, PT4,PT6. Of these patterns the pattern PT2 has a contour which cannot beregarded as a convex shape.

[0163] Next, vertical components and horizontal components of thepattern image are searched (step S2). Specifically, a gray scale data isscanned in a vertical direction and a horizontal direction in the imageImg2 to calculate coordinates of the horizontal and vertical directionsof local peaks in tone thereof. FIGS. 4A and 4B are diagrams visiblyshowing the calculated coordinates. FIG. 4A schematically shows edgedata of the horizontal direction obtained by searching the edges of thevertical direction, and FIG. 4B schematically shows the edge data of thevertical direction obtained by searching the edges of the horizontaldirection. More specifically, the peaks are searched at an interval often pixels in the vertical and horizontal directions to obtain asmoothed differential value of the gray scale data obtained in therespective searches and to specify a position in the vicinity of amaximum value.

[0164] Next, discriminant analysis to the obtained vertical andhorizontal coordinates is performed (step S3). Steps are performedcomprising: regarding two positions as the same, when F value defined bythe following equation (1) is not more than a predetermined value; andon the other hand, regarding the positions as independent positions,when the F value exceeds the predetermined value.

F=V_(int er)/V_(int ra)   Equation (1),

[0165] wherein

V _(int er)=Var({overscore (x)} ₁ ,{overscore (x)} ₂ ,{overscore (x)} ₃, . . . ,{overscore (x)} _(N))

V _(int ra)=Ave(V ₁ ,V ₂ , . . . ,V _(N))

[0166] {overscore (x)}₁,{overscore (x)}₂,{overscore (x)}₃, . . .,{overscore (x)}_(N) and V₁,V₂, . . . ,V_(N) indicate an average valueand variance of an x coordinate of each class, when a sequence of pointsis rearranged in accordance with a size of the x coordinate andthereafter the sequence is divided into N classes. This value at a timewhen F is maximized gives the positions of the vertical components ofthe pattern edge after the discriminant analysis.

[0167] It is to be noted that Var( ) means the calculation of varianceof the value within ( ), and Ave( ) means the calculation of the averagevalue within ( ).

[0168] Furthermore, the calculation is also similarly performed withrespect to a y coordinate of the sequence of points.

[0169]FIGS. 5A and 5B show discriminant analysis results of thecoordinate data shown in FIGS. 4A and 4B, respectively. FIG. 5A showsthe horizontal components of the pattern edge, and FIG. 5B shows thevertical components of the pattern edge. Furthermore, FIG. 6 is adiagram in which the horizontal components of FIG. 5A are synthesizedwith the vertical components of FIG. 5B.

[0170] Next, the lattice is generated on the image using the result ofthe discriminant analysis (step S4). Specifically, the vertical andhorizontal coordinates finally regarded as independent positions shownin FIG. 6 are used to generate a lattice L2 on the image as shown inFIG. 7. In this stage, the lattice L2 is a polygon having edges to whichpredetermined direction components are given. In the present embodimentall the predetermined direction components are the horizontal andvertical components. Furthermore, a length Lij and weight function wijare imparted to each edge of the lattice L2, and stored as table data ina storage device (see FIG. 42). Here, the weight function wij is afunction which can be expressed in the following equation (2) with thenumber nij of local peaks of gray scale value data attributed to eachedge of the lattice L2.

wij=nij/Lij   Equation (2)

[0171] It is to be noted that the predetermined direction components arenot limited to the horizontal and vertical components. The direction mayform an angle integer times as much as 0° to 45° with respect to areference direction which can arbitrarily be set to an image direction.

[0172] Next, a polygon referred to as “lattice animal” is combined onthe lattice L2 generated on the image Img2 in this manner (step S5).Here, the “lattice animal” means a polygon prepared by disposing theedges of the arbitrary number of lattice elements adjacent to oneanother to synthesize the elements. A method of automatically generatingthe polygon is described, for example, in Discrete Mathematics 36 (1981)pp. 191 to 203 by D. H. Redelmeier, “Introduction to Percolation Theory”by D. Stauffer, Taylor & Francis, London & Philadelphia, 1985 appendix Aand the like. In the present embodiment, necessary number of latticeanimals is beforehand generated, and the contours of the animals arerepresented by chain codes described in Computing Surveys, vol. 6, No.1, pp. 57 to 97 (1974) by H. Freeman. Then, the animals are numberedwith the numbers of longitudinal and lateral edges, and beforehandstored as an “animal table” in the storage device (see FIG. 42). Onerepresentation example of this chain code is shown in FIG. 8A, and someexamples α1 to α4 of the lattice animal are shown in FIGS. 8B to 8E.

[0173] A specific procedure for superposing the lattice animals upon oneanother will be described with reference to FIGS. 2, 9, and 10. First,one arbitrary lattice point A is selected from all the lattice points(FIG. 2, step S501). Explaining the lattice L2 shown in FIG. 7 as anexample, a lattice point p2, for example is selected as shown in FIG. 9.Next, an arbitrary lattice animal a is selected from the “animal table”(FIG. 2, step S502). In the example shown in FIG. 9, a lattice animalα10 is selected as the lattice animal a. Next, the lattice (lattice L2in FIG. 9) is traced from the selected lattice point A by the chain codeof the selected lattice animal. At this time, the pre-stored weights aresuccessively added to the respective edges of the traced lattice, andthe added result is defined as an existence probability Ra of thelattice animal a and then stored in the storage device (see FIG. 42)(step S503). Next, another lattice point B is selected from the latticepoints which do not belong to the lattice animal which has alreadyselected (step S504). In the example shown in FIG. 9, for example, alattice point p4 is selected from the lattice points not belonging tothe lattice animal α10 whose start point is the lattice point p2. Next,another arbitrary lattice animal is selected newly as a lattice animal bfrom the animal table (step S505). As an example of the lattice animalb, FIG. 9 shows a lattice animal α12. Subsequently, the lattice istraced from a lattice point B by the chain code corresponding to thelattice animal b (step S506). In the example shown in FIG. 9, thelattice point p4 is used as the start point to trace the lattice L2 bythe chain code of the lattice animal α12. Additionally, at this time,when the lattice point or edge belonging to the lattice animal b (α12 inthe example of FIG. 9) is already occupied by another lattice animal(e.g., the lattice animal α10 of FIG. 9) (step S507), the currentlattice animal b (lattice animal α12 in FIG. 9) is discarded (stepS508), and one lattice animal b is selected newly (step S505). When thelattice point or edge belonging to the existing lattice animal b is notoccupied by another lattice animal yet (step S507), the lattice istraced from the lattice point B with the chain code corresponding to thelattice animal b, and an existence probability Rb is calculated andstored in the storage device (see FIG. 42) (step S509).

[0174] When the above-described procedures (steps S505 to S509) arerecursively repeated for the whole lattice (step S510), the animals aredisposed in the whole lattice. As a result, the calculated existenceprobabilities are obtained for all the lattice animals disposed in thewhole lattice at this time.

[0175] Next, an integrated value of all the existence probabilities withrespect to all the lattice animals calculated in this manner iscalculated and defined as an integrated value T. Furthermore, latticeanimal arrangement information is constituted by the number of latticeanimals, the start point coordinate of each lattice animal, thenumerical order of each lattice animal, and the integrated value T andprovided with a label (e.g. label C1), and the information is stored inthe storage device (see FIG. 42) (step S511).

[0176] Next, when the lattice animal which can be disposed using thelattice point A as the start point exists in the animals other than thelattice animal a (step S512), the lattice animal is newly selected asthe lattice animal a (step S513), and the above-described steps S502 toS511 are repeated.

[0177] Furthermore, if there are lattice points which have not beenselected as the lattice point A yet in all the lattice points (stepS514), one of the points is newly selected as the lattice point A (stepS515), and the above-described steps S502 to S513 are repeated.

[0178] By the repetition of these procedures, the integrated value T ofthe existence probabilities can be obtained with respect to a way ofarrangement of all the lattice animals which can be arranged in thewhole lattice.

[0179] Finally, the arrangement of the lattice animals in which amaximum value of T is obtained is selected from all the arrangement ofthe lattice animals (step S516).

[0180] One example of the animal arrangement finally selected in thismanner is shown in FIG. 10. As shown in the drawing, outlines RF2, RF4,and RF6 of the contours of the patterns were calculated by a figureconstituted only of the horizontal/vertical edges.

[0181] Turning back to FIG. 1, a Voronoi diagram is prepared withrespect to the vertices of each lattice animal existing on the outerperiphery with respect to the outlines of the pattern contoursconstituted by the above-described procedure (step S6). FIG. 11 shows aVoronoi diagram VF2 prepared in this manner.

[0182] Next, as shown in FIG. 12, the Voronoi regions including thevertices attributed to the same animal are synthesized with respect tothe respective Voronoi regions of the prepared Voronoi diagram VF2, andboundaries of synthesized regions AR2, AR4, AR6 are defined as thespheres of influence of the respective animals to obtain the boundariesin searching the edge as described later (step S7).

[0183] Subsequently, as shown in FIG. 13, the vertices of the latticeanimal which do not exist in corners are removed.

[0184] Next, one of the regions AR2, AR4, AR6 divided in this manner bythe Voronoi diagram is selected (step S8), all diagonal lines which donot intersect with one another are drawn in the animal existing in theregion, and the animal is divided into triangles (step S9). Furthermore,the respective vertices of the animal are point-colored in red (R),green (G), and blue (B) following a description order of the chain code(step S10). At this time, the respective vertices of the triangles arecolored in such a manner that the vertices disposed adjacent to eachother via one edge do not have the same color. FIG. 14 shows a result ofthe dividing and point-coloring of the animal in this manner withrespect to the region AR of FIG. 13.

[0185] Subsequently, the triangles which share the vertex colored in Rare synthesized to prepare a new figure SP4 as shown in FIG. 15. Theanimal arrangement was thus divided into the star-shaped (convex herein)polygon (step S11).

[0186] Subsequently, the position coordinate of a core (kernel) iscalculated by algorithm of Lee-Preparata described in Info. Proc. Lett.7, pp. 189 to 192 (1978) with respect to each star-shaped polygon (stepS12). As shown in FIG. 16, the gray scale value of an original image issuccessively checked from the positions of kernels CN2, CN4 toward theouter periphery of the lattice animal (searching directions SD2 a to SD2c) in a chain code order of the animal (see FIG. 8A) to the boundary ofthe sphere of influence (SP4 in FIG. 16) of the lattice animal. Thepattern edge position is calculated in accordance with the existing edgesearching method, and each calculated edge position is stored in thestorage device (see FIG. 42) (step S13). In this case, when a pluralityof edges are detected, only one edge closest to the position of thekernel is selected. In the present embodiment, a threshold value methodwas used, and a threshold value was set to 50%. By this procedure, edgepoint sequence data remarkably close to an actual pattern edge positionis calculated in the form of chain arrangement in one region. To searchthe edge using the respective kernels CN2, CN4 as the start points, whenthe embodiment of the searching method of the pattern edge according tothe present invention described later is used in addition to theabove-described method, the position of the edge can further preciselybe calculated.

[0187] Subsequently, the steps S8 to S13 are also performed with respectto the other spheres of influence (FIG. 13, AR4, AR6) (steps S14, S15),and the contour data of all the patterns included in the image islabeled and outputted (step S16). Accordingly, for example, thethreshold value method can be used to exactly calculate the contour dataof all the patterns in the image to be inspected without any wrongdetection.

[0188] According to the present embodiment, it is possible to outputpattern edge data in the form of the chain arrangement for eachindependent pattern from image data including the pattern in acomplicated shape without performing the intricate image matching,referring to enormous amounts of CAD data, or manually dividing theregion.

[0189] There exists a high-rate algorithm of the order of O (nlogn) (ndenotes the number of vertices of the figure which is the object) orless for all the procedures of the Voronoi diagram preparation, thestar-shaped polygon generation, the searching of the kernel and the edgesearching which are used in the present embodiment. Therefore, by theuse of the algorithm, an image processing time can largely be reduced.

[0190] It is to be noted that in the present embodiment, a smoothingdifferential calculus was used in searching the horizontal/verticalcomponents of the edges, the methods such as the threshold value methodor a subtractive color process may also be used instead. In the presentembodiment, the Voronoi diagram was prepared to generate the sphere ofinfluence of the plurality of patterns existing in the image. However,when there is only one pattern in the image, or when the region isdesignated beforehand, this region division is unnecessary. Furthermore,when the contour data does not require high accuracy, the animalarrangement is accepted to obtain the calculated maximum integratedvalue T up to the step S5 of FIG. 1, and the vertex coordinate of theanimal may also be used as the contour data of the pattern as such.

(2) Second Embodiment

[0191] Next, a second embodiment of the present invention will bedescribed with reference to FIGS. 17 to 21.

[0192] In the present embodiment, there is provided an extracting methodof the pattern contour in a case in which a plurality of patterns havingthe contours of schematically convex types exist on the image. In thiscase, since the kernel can also be set in any position in the pattern,the dividing procedure into the star-shaped polygon in the firstembodiment (FIG. 1, steps S9 to S11) can be omitted.

[0193]FIG. 17 shows one example of the image including a plurality ofpatterns PT32 which have schematically convex contours ED.

[0194] In the same manner as in the first embodiment, for example, aninspection object image Img4 is acquired, and the edge components in thehorizontal and vertical directions of the image Img4 are extracted asshown in FIGS. 18A and 18B (FIG. 1, step S2).

[0195] Next, the extracted edge components are classified into fourlevels in the vertical direction and ten levels in the horizontaldirection, a lattice L4 is generated based on a schematic edge positionas shown in FIG. 19A, and further the animal table is referred to incalculating an animal arrangement (AD4) having a higher probability asshown in FIG. 19B.

[0196] Next, a Voronoi diagram VF8 is prepared with respect to thevertex of the animal as shown in FIG. 20A, and further the regionsbelonging to the same animal are unified to define a new Voronoi regionAR8 as shown in FIG. 20B.

[0197] Furthermore, as shown in FIG. 21, the pattern edges are searchedalong radial directions SD6 toward each boundary from one point (kernel)inside the animal in each region, and the contour data is extracted.With regard to search of the edge from each kernel which is the startpoint, the searching method of the pattern edge according to theembodiment of the present invention described later can be used inaddition to the method according to the related art. In this case, theposition of the edge can more precisely be calculated.

[0198] As described above, according to the present embodiment, when aplurality of patterns having the contours of the schematic convex typesexist on the image, it is possible to accurately acquire the data of thepattern contour in a simpler procedure.

(3) Third Embodiment

[0199] A third embodiment of the present invention will be describedwith reference to FIGS. 22A to 24. In the present embodiment, there isprovided an extracting method of the pattern contour, in which theacquired image includes the single pattern only but the contour of thepattern is not regarded as the convex shape.

[0200] First, the schematic contour of the pattern to be inspected isrepresented by the lattice animal in a procedure similar to that of thefirst embodiment (FIG. 1, steps S1 to S5). As a result, one example ofthe lattice animal arrangement is obtained with respect to the singlepattern. One example of the lattice animal arrangement thus obtained isshown in FIG. 22A. In the present embodiment, since only the pattern tobe inspected is included in the image, it is not necessary to calculatethe sphere of influence of the pattern any more. Therefore, theprocedure for calculating the Voronoi diagram (FIG. 1, steps S6 to S8)can be omitted.

[0201] The diagonal lines are drawn with respect to the obtained latticeanimal to perform the triangulation (FIG. 1, step S9). A lattice animalAD6 shown in FIG. 22A can be divided into the triangles, when twelvediagonal lines DL11 to DL22 are drawn as shown in FIG. 22B.

[0202] Subsequently, in the same manner as in the first embodiment, thevertices of each triangle are point-colored in three colors as shown inFIG. 23A (FIG. 1, step S10), and further the triangles sharing thevertex colored, for example, in R are integrated to perform the divisionby the star-shaped polygon (FIG. 1, step S11). Subsequently, theposition of each kernel is calculated with respect to each star-shapedpolygon in the same manner as in the first embodiment (FIG. 1, stepS12). Accordingly, as shown in FIG. 23B, the start point of the edgesearching and the edge searching region without any wrong detection wereobtained.

[0203] Thereafter, although not especially shown, in the same manner asin the first embodiment, the edge is searched toward the outer peripheryof each star-shaped polygon from each kernel (see FIG. 1, step S13).

[0204] As described above, according to the present embodiment, evenwith the pattern including the contour which cannot be regarded as theconvex shape, when the image including the single pattern only isobtained, the data of the pattern contour can be acquired by a simplerprocedure and for a shorter inspection time. It is to be noted that forthe edge searching, with the use of the searching method of the patternedge according to the embodiment of the present invention describedlater, the edge position can further precisely be detected.

(4) Fourth Embodiment

[0205] A fourth embodiment of the present invention will be describedwith reference to FIGS. 24 to 26. FIG. 24 is a flowchart showing aschematic procedure of the extracting method of the pattern contourincluding the image processing method of the present embodiment, andFIGS. 25A to 26E show examples of the image processed by the procedureshown in FIG. 24.

[0206] First, the gray scale image data of the pattern which is theobject of the inspection is acquired, for example, by SEM (FIG. 24, stepS30). One example of the acquired image data is shown in FIG. 25A. Animage Img6 shown in the drawing includes eleven patterns in totalincluding patterns PT8, PT14, PT16 having the contours which cannot beregarded as the convex shapes.

[0207] Next, as shown in FIG. 25B, a pattern edge EP2 is searched alonga boundary AR26 of the inspection image Img6 (step S31). To search thepattern edge, the smoothing differential calculus was used to define thepeak position after the smoothing differentiation as the pattern edge.

[0208] Next, a Voronoi diagram VF10 is prepared with respect to the edgepoint EP2 found on the boundary AR26 as shown in FIG. 25C (step S32).

[0209] Next, as shown in FIG. 25D, the edge searching by the smoothingdifferentiation is again performed along each edge of the Voronoidiagram VF10 (step S33).

[0210] Next, the edge including a pattern edge point EP4 is removed fromthe respective edges of the Voronoi diagram VF10 (steps S 36, S37), andfurther isolated edges and branches are removed (step S38). Accordingly,as shown in FIG. 26A, the whole gray scale image Img6 is divided intofive regions RG1 to RG5.

[0211] Next, with respect to the respective regions RG1 to RG5, in thesame manner as in the steps S31 and S32, the edge point is searchedalong the boundary of the region (step S40), and the Voronoi diagram isprepared with respect to the searched edge point sequence again (stepS41). FIG. 26B representatively shows a Voronoi diagram VF12 a preparedagain with respect to the lower region RG3.

[0212] Next, the edge is searched along a Voronoi edge in the samemanner as in the step S32 (step S42). An edge point EP6 obtained as aresult of the edge searching is shown in FIG. 26C.

[0213] Next, the Voronoi edges, and the isolated edges and branchesincluding the edge point EP6 are removed in the same manner as in thesteps S36 to S38 (steps S43 to S45). As a result, as shown in FIG. 26D,the original region RG3 is further divided into three regions RG6 toRG8.

[0214] Furthermore, the above-described procedure is recursivelyperformed with respect to all the divided regions, until the shape ofeach divided region becomes unchanged (steps S48, S49, S40 to S47). As aresult, as shown in FIG. 26E, the pattern image Img6 was divided into alarge number of regions RG1, RG2, RG4 and RG5, RG7 to RG15 so that eachregion finally includes one pattern edge.

[0215] As described above, according to the present embodiment, with theinspection image including a plurality of patterns including thepatterns having the contours which cannot be regarded as the convexshape, the inspection image can be divided so as to include each patternedge.

[0216] Finally, the searching method of the pattern edge in the first tothird embodiments is used to search the edge for each region.Accordingly, all the pattern edges can be acquired as the chainedarrangement data for each region. It is to be noted that with the use ofthe pattern edge searching method in ninth and tenth embodimentsdescribed later, the edge position can more precisely be calculated.

(5) Fifth Embodiment

[0217] Next, a fifth embodiment of the present invention will bedescribed with reference to FIGS. 27 to 29C. FIG. 27 is a flowchartshowing the schematic procedure of the image processing method in thepresent embodiment. FIGS. 28A to 28D and FIGS. 29A to 29C are diagramsshowing the examples of the image processed by the procedure shown inFIG. 27. According to the present embodiment, there is provided theextracting method of the pattern contour including the image processingmethod in a case in which the pattern edge intersecting with theboundary of the acquired gray scale image does not exist in the image.

[0218] First, after acquiring an image Img8 of the pattern as shown inFIG. 28A (FIG. 27, step S51), as shown in FIG. 28B, first edge searchingis performed in a longitudinal direction SD10 over the whole image Img8and in a lateral direction SD8 over the whole image Img8 (step S52). Inthe present embodiment, each edge direction is set in a position where alength and width of the image Img8 are divided at a golden ratio, but itis possible appropriately change the position and number of thedirection.

[0219] As a result of the edge searching, the position coordinate ofpattern edges EP8 was obtained as shown in FIG. 28C.

[0220] Next, the Voronoi diagram VF is prepared with respect to thesearched edge point (step S53). For the prepared Voronoi diagram, as inVF14 shown in FIG. 28D, substantially parallel straight lines areobtained.

[0221] Next, the edge is searched along the Voronoi edge of the preparedVoronoi diagram (step S54), and further the Voronoi diagram is preparedwith respect to obtained edge points EP10 (step S55). As a result, aVoronoi diagram VF16 shown in FIG. 29A was obtained.

[0222] Next, as shown in FIG. 29B, the edge searching is performed alongthe edges of the Voronoi diagram VF16 again (step S56), the Voronoiedges including searched edge points EP12 are deleted (steps S57, S58),and further the isolated edge and branch are removed (step S59). As aresult, as shown in FIG. 29C, the image Img8 is divided into sub-regionsRG21 to RG24 each including one curve constituted of the sequence ofedge points.

[0223] Thereafter, the searching method of the pattern edge in thesecond embodiment is used to perform the edge searching for each region.Accordingly, all the pattern edges can be acquired as the chainedarrangement data for each region. It is to be noted that the searchingmethod of the pattern edge in the ninth and tenth embodiments describedlater can be used to more precisely calculate the position of the edge.

(6) Sixth Embodiment

[0224] Next, a sixth embodiment of the present invention will bedescribed. According to the present embodiment, there is provided theextracting method of the pattern contour including another imageprocessing method in a case in which the pattern edge intersecting withthe boundary does not exist in the acquired image.

[0225] For example, the pattern edge intersecting with the boundary ofthe image Img8 does not exist as shown in FIG. 30A. In this case, anoptical microscope used in acquiring the image or SEM whosemagnification is set to be higher is used to acquire the image again.Then, as shown in FIG. 30B, an image Img9 is obtained whose pattern edgeintersects with the boundary. Therefore, thereafter, the imageprocessing in the first to fourth embodiments is used to divide theregion in such a manner that each region includes the single patternonly. Moreover, by the edge searching method in the first to thirdembodiments or in the ninth or tenth embodiment described later, theedge position may be detected.

(7) Seventh Embodiment

[0226]FIG. 31 is a flowchart showing the schematic procedure of theimage processing method in a seventh embodiment, and FIGS. 32A to 32Eshow the examples of the image processed by the procedure shown in FIG.31.

[0227] According to the present embodiment, a step of searching thepattern edge in the longitudinal and lateral directions at an intervalwhich is about half of a minimum pattern pitch beforehand in the wholeacquired image is added to the fourth embodiment. That is, as shown inFIG. 32A, the pattern edge is searched in a longitudinal direction SD12and lateral direction SD14 at an interval which is about half of theminimum pattern pitch in the whole gray scale image Img6 (FIG. 31, stepS62).

[0228] Thereafter, in the same manner as in the fourth embodiment, theprocedures of: the generation of the Voronoi diagram VF16 (FIG. 32B)(FIG. 31, step S63); the edge searching along the Voronoi edge (FIGS.32C, 31, steps S64 and S65); and the integration of the Voronoi regionsand the removing of the branches (FIGS. 32D, 31, steps S66 to S68) arerecursively repeated (steps S 69 to S72, S63 to S68).

[0229] As described above, according to the present embodiment, since alarge number of point sequences belonging to the pattern edge areobtained beforehand in step S62, the procedure for recursion can largelybe omitted. For example, in comparison of FIG. 31 with FIG. 24, thesteps S33 to S38, S40 and S41 of FIG. 24 are not necessary. Even by thissimple procedure, as shown in FIG. 32E, the image Img6 can be dividedinto nine regions RG31 to RG39 so that the single pattern only isincluded in each region.

[0230] After the image processing by the above-described procedure, whenthe searching method of the pattern edge in the first or thirdembodiment or in the ninth or tenth embodiment described later is usedto search the edge for each region, all the pattern edges can beacquired as the chained arrangement data for each result.

(8) Eighth Embodiment

[0231] According to an eighth embodiment, there is provided a method ofapplying the result of the division into the regions by the first toseventh embodiments to pattern matching.

[0232]FIG. 33 is a flowchart showing the schematic procedure of theimage processing method in the eighth embodiment. FIGS. 34A to 34F areexplanatory views specifically showing the image processing method shownin FIG. 33.

[0233] First, a reference image is acquired as a reference of patternmaterial from CAD data with respect to the pattern of the inspectionobject (FIG. 33, step S81). One example of the reference image is shownin FIG. 34A. In the drawing, a reference image Rimg10 includes six holepatterns PT30, PT32, PT34, PT36, PT38, PT40. In these patterns, thepattern PT30 in a circled position in FIG. 34A is designated as theinspection object pattern (FIG. 33, step S82).

[0234] Next, with respect to the whole reference image Rimg10, as shownin FIG. 34B, in the same manner as in the fifth embodiment, a Voronoidiagram VF18 is prepared so that each region includes the single pattern(FIG. 33, step S83), and the respective vertices are numbered with{circle over (1)} to {circle over (10)} (FIG. 33, step S84).

[0235] Next, the inspection image including the hole pattern PT38 whichis the inspection object is acquired (FIG. 33, step S85). The exampleImg10 of the inspection image is shown in FIG. 34C.

[0236] Next, also with respect to the inspection image Img10, in thesame manner as in the reference image Rimg10, the Voronoi diagram isprepared so that each region includes the single pattern only (FIG. 33,step S86), and the respective vertices are numbered with {circle over(1)} to {circle over (10)} (FIG. 33, step S87). The result is shown inFIG. 34D. It is to be noted that in the present embodiment the way ofthe numbering of the reference image Rimg10 is not especially associatedwith that of the inspection image Img10.

[0237] Next, there are extracted the Voronoi diagram VF18 of thereference image Rimg10 and a Voronoi diagram VF20 of the object imageImg10 only, and rotary movement or translational movement is relativelyperformed so that the position of the edge of the Voronoi diagram VF18may be closest to that of the Voronoi diagram VF20 of the object image,thereby associating the Voronoi vertices with one another (step S88).

[0238] Thereafter, as shown in FIG. 34E, a region RG42 corresponding toa Voronoi region RG40 (dotted area) including the inspection objectpattern PT30 in the reference image Rimg10 is defined in the inspectionimage Img10 (step S89).

[0239] Finally, as shown in FIG. 34F, the pattern included in the regionRG42 defined in the inspection image Img10 is determined as theinspection object pattern PT30 in the inspection image (step S90).

[0240] In the example shown in FIGS. 34A to 34F, the Voronoi diagramswere matched with one another so as to minimize a residual of thepositions of the edges. However, when the number of patterns included inthe image increases or becomes complicated, the calculation requiresmuch time in this method. In this case, when only connectivity of theVoronoi regions is noticed, the pattern matching can be performed moresimply.

[0241]FIGS. 35A to 35E are explanatory views of this simple matchingmethod. First, as shown in FIGS. 35A and 35B, the Voronoi diagrams ofRimg10 and Img10 shown in FIGS. 34B and 34D are rewritten to graphs VF19and VF21 in which the length of each edge is neglected. Here, theinspection object pattern PT30 designated beforehand exists in a squarewhose vertices are points {circle over (2)}, {circle over (3)}, {circleover (7)}, and {circle over (5)} in a reference image RImg11.

[0242] Next, the graph VF21 of FIG. 35B corresponding to the inspectionimage Img10 is rotated/translated so as to agree with the graph VF19 ofFIG. 35A. In the present embodiment, when the graph VF21 of FIG. 35B isrotated by about 90° in a clockwise direction, a graph VF22 shown inFIG. 35C is acquired.

[0243] Next, in the graph VF22, the vertices to define a partcorresponding to the region to be inspected in the graph VF19 in thereference image of FIG. 35A are acquired. As a result, as shown in FIG.35D, a region surrounded with vertices {circle over (3)}, {circle over(9)}, {circle over (5)}, and {circle over (2)} is obtained.

[0244] As described above, the pattern in the region surrounded with thevertices {circle over (3)}, {circle over (9)}, {circle over (5)}, and{circle over (2)} in the original Voronoi diagram VF20 shown in FIG. 35Ecan be identified as the inspection object pattern.

[0245] According to the image processing method of the presentembodiment, it is also possible to automatically find a specific partfrom the image. This respect will be described in more detail withreference to FIGS. 36A to 36F.

[0246] A partial region Rimg10 a is cut out beforehand from thereference image Rimg10 shown in FIG. 36A as shown in FIG. 36B, andthereafter the Voronoi diagram is prepared with respect to the wholereference image Rimg10 together with the cut-out region Rimg10 a. FIG.36C shows a Voronoi diagram VF18 a prepared with respect to the cut-outregion Rimg10 a.

[0247] Subsequently, with respect to the image to be inspected Img10(FIG. 36D), the Voronoi diagram VF20 is also prepared (FIG. 36E).

[0248] Next, a part whose geometric position most agrees with that ofthe Voronoi diagram VF18 a shown in FIG. 36C is searched in the Voronoidiagram VF20 of the image to be inspected Img10. As shown in FIG. 36F, arectangular region RG42 circumscribed with the Voronoi diagram VF18 acan be defined as the region which includes the pattern to be inspectedin the image to be inspected Img10.

[0249] According to the present embodiment, it is possible to execute apattern matching in which irregular arrangement information of a patternis used as a template. Therefore, when a plurality of the same patternsexist in the inspection object image, one specific pattern can bedesignated with high accuracy. Furthermore, it is also possible to findany defect of the pattern in the image to be inspected by comparing theVoronoi diagram of the reference image after the matching with theVoronoi diagram of the image to be inspected and by checking the edgesand vertices which do not match each other. .

(9) Ninth Embodiment

[0250] Next, a ninth embodiment of the present invention will bedescribed with reference to FIGS. 37 and FIGS. 38A to 38C. According tothe present embodiment, there is also provided a method of preferablydetecting the edge of the pattern which has a complicated contour shape.

[0251]FIG. 37 is a flowchart showing the schematic procedure of the edgesearching method in the present embodiment, and FIGS. 38A to 38C aremore specific explanatory views of the edge searching method shown inFIG. 37.

[0252] First, the image of the pattern to be inspected is acquired (FIG.37, step S101). For explanation of the present embodiment, the patternPT44 shown in FIG. 46 is used again.

[0253] A partial enlarged view of the image of the pattern to beinspected PT44 is schematically shown in FIG. 38A. Here, it is assumedthat the coordinates of vertices ST2 and ST4 of the edge SL2 of thepolygon indicating the schematic edge position of the pattern PT44 isalready given by the method described, for example, in theabove-described embodiment.

[0254] Next, the position coordinates of a region to be inspected SRincluding a pattern PT44 a which is a part of the pattern PT44 isrepresented on a complex plane in which the x-axis thereof is a realaxis and the y-axis thereof is an imaginary axis (FIG. 37, step S102).

[0255] Subsequently, on the complex plane, a start point is set, forexample, at the position of a point GP2 shown in FIG. 38A (FIG. 37,steps S103 and S104). This start point GP2 is a simulated-source pointin hydrodynamics.

[0256] Next, a point SN2 at the position of the mirror image of thesource point GP2 with respect to the edge SL2 is calculated, and thepoint is set on the complex plane as shown in FIG. 38B (FIG. 37, stepS105). The calculated point SN2 is a simulated-sink point in thehydrodynamics.

[0257] Next, assuming that the point GP2 is the source point and thepoint SN2 is the sink point, an ideal fluid field is defined on thecomplex plane (FIG. 37, step S106). For this field of stream, a solutionis analytically given, and a function form is described in detail inpage 278 of “Conformal Maps” authored by Akira Watanabe (published byAsakura Shoten, 1984). A complex potential W1 representing the streamfield in this case is a complex function in the form of the followingequation:

W1=log{(e ^(z)−1)/(e ^(z)+1)}  Equation (3)

[0258] Next, a contour line with respect to the real part of theequation (3), that is, a streamline is calculated (FIG. 37, step S107).A calculation result is, for example, a curve group FL shown in FIG.38C.

[0259] Thereafter, by executing the edge searching, for example, basedon the threshold value method in the direction along each curve of thecurve group FL, the positions of the pattern edge are extracted (FIG.37, step S108).

[0260] In the present embodiment, for the edge searching, the thresholdvalue method along the searching direction is used, but the presentinvention is not limited to this method. For example, a differencefilter, peak searching method, and the like may also be used.

[0261] Moreover, in the present embodiment, the extracting searchingdirection is determined based on the stream field of a two-dimensionalfluid, but the edge searching direction may also be determined based ona two-dimensional electric field in which positive/negative pointcharges are arranged, instead of concepts of the source and sink points.

[0262] Furthermore, the image to be inspected acquired by scanning typeprobe microscopes such as the optical microscope can also appropriatelybe used with respect to the inspection image.

(10) Tenth Embodiment

[0263] Next, a tenth embodiment of the present invention will bedescribed with reference to FIGS. 39 and 40A, 40B. FIG. 39 is aflowchart showing the schematic procedure of the edge searching methodin the present embodiment, and FIGS. 40A and 40B are diagrams morespecifically showing the edge searching method shown in FIG. 39. Asshown in FIG. 40A, also in the present embodiment, the pattern PT44shown in FIG. 46 is assumed as the pattern to be inspected. It is alsoassumed that the coordinates of the vertices ST2 and ST4 of the edge SL2of the polygon representing the schematic edge position of the patternPT44 are already given.

[0264] In the same manner as the ninth embodiment, first, afteracquiring the image of the pattern to be inspected (FIG. 39, step S111),the position coordinate of the region to be inspected SR including thepattern PT44 a which is a part of the pattern PT44 is transformed intothose on the complex plane (FIG. 39, step S112).

[0265] Next, one searching start point PC2 is selected in the region tobe inspected SR (FIG. 39, step S113). In the present embodiment, apositive point charge is simulated by this start point PC2, a chargedistribution having a linear density on a line segment of the startpoint PC2 is disposed in an simulated manner, and an electrostaticpotential at this time is calculated (FIG. 39, step S114).

[0266] The electrostatic potential at this time is superposition of anelectrostatic potential W2 supplied by the point charge upon anelectrostatic potential W3 with respect to a linear negative chargedistribution. A line of electric force obtained as a result is defined(FIG. 39, step S115). Examples of these lines of electric force areshown in a curve group EL of FIG. 40B.

[0267] Then, the edge searching is performed, for example, based on thethreshold value method in the direction along each curve of the curvegroup EL to extract the position of the pattern edge (FIG. 39, stepS116).

[0268] Also in the present embodiment, in addition to the thresholdvalue method along the searching direction, the difference filter, peaksearching method, and the like can be used in searching the edge.

[0269] Moreover, in the present embodiment, the edge searching directionhas been determined based on the two-dimensional electric field in whichthe positive/negative charges are disposed. However, the direction mayalso be determined based on the stream field of the two-dimensionalfluid in which the source/sink is disposed, for example, instead of thepoint charge.

(11) Eleventh Embodiment

[0270] Next, an eleventh embodiment of the present invention will bedescribed with reference to FIG. 41. According to the presentembodiment, there is provided a scanning method of a probe using theedge searching method in the ninth and tenth embodiments. The methodwill be described hereinafter using an electron beam as the probe. Forthe specific constitution of a probe inspection apparatus, refer to atwelfth embodiment described later (FIG. 42).

[0271]FIG. 41 is a flowchart showing the schematic procedure of theprobe scanning method and edge searching method in the presentembodiment. As shown in the drawing, first, a control system of CD-SEM(see FIG. 42) is allowed to read the data of the vertex coordinate ofthe polygon indicating the schematic edge position of pattern to beinspected and the data of the coordinate of the start point of the edgesearching (step S121).

[0272] Next, the position coordinate of the region to be inspectedincluding the pattern to be inspected is transformed into that on thecomplex plane in which the x-axis thereof is a real axis and the y-axisthereof is an imaginary axis (step S122).

[0273] Subsequently, the source point and sink point are set on thecomplex plane in the same manner as in the ninth embodiment to definethe ideal fluid field (steps S123 to S125).

[0274] Next, the streamline of the ideal fluid field is calculated, andthe coordinate positions are stored in the storage device (see FIG. 42)connected to the control system (step S126). The calculation result ofthe streamline is the same as that of the curve group FL of FIG. 38C.

[0275] Subsequently, the scanning signal of the probe is generated basedon the streamline coordinate stored in the storage device, and the probeis scanned to acquire the secondary electron signal in synchronizationwith the scanning signal (step S127).

[0276] Furthermore, the edge position is defined from the profile of theacquired secondary electron signals, for example, by the threshold valuemethod, and the position information of the pattern edge is extracted(step S128).

[0277] In the present embodiment, the probe microscope is described, butthe present invention is never limited to this apparatus. The presentinvention can be applied to all inspection apparatuses for scanning theprobe to acquire the image, such as an STM, an AFM, and a laser scanningmicroscope.

(12) Twelfth Embodiment

[0278] Next, a twelfth embodiment of the present invention will bedescribed with reference to FIG. 42. According to the presentembodiment, there is provided a pattern inspection apparatus toimplement the first through eleventh embodiments.

[0279]FIG. 42 is a block diagram showing the schematic constitution ofthe pattern inspection apparatus according to the present embodimenttogether with an apparatus connected to the inspection apparatus. Apattern inspection apparatus 1 shown in the drawing comprises anelectronic optical system controller 22, a computer 20, a memory 24, adisplay 26, and an input device 28.

[0280] An apparatus 10 also shown in FIG. 42 constitutes a probeinspection apparatus in the present embodiment, and includes a stage 14on which a substrate W is mounted, an electronic optical system 12, asecondary electron detector 16, and a signal processor 18. Theelectronic optical system 12 generates an electron beam EB to irradiatethe substrate W on which a certain fine pattern is formed as theinspection object with the electron beam EB. The secondary electrondetector 16 detects secondary electrons/reflected electrons/backwardscattered electrons generated from the surface of the substrate W byirradiation with the electron beam EB. The signal processor 18 convertsan analog signal constituted of the secondary/reflected/backwardscattered electrons detected by the secondary electron detector 16 intoa digital signal, amplifies the signal, and supplies the signal as theimage data of the pattern to be inspected to the computer 20.

[0281] In the memory 24, program is stored in the form of a recipe fileto execute various operation processes for the above-describedembodiments. These operation processes include: difference processing toextract horizontal and vertical components of the pattern edge;processing to perform the matching of the lattice animal; geometriccalculation to calculate the Voronoi diagram; processing to compare theVoronoi diagrams with each other; processing to judge whether or not thepoint including the arbitrary coordinate exists on the edge or vertex ofthe Voronoi diagram; processing to calculate the position of the patternedge from the gray scale value of the image; processing to calculate thecomplex or electrostatic potential based on the coordinate data of thepolygon indicating the schematic position of the pattern edge; andprocessing to calculate the coordinate data of the edge searchingdirection from the calculated complex or electrostatic potential.

[0282] The memory 24 also stores various data such as the image data ofthe inspection object pattern supplied from the signal processor 18 viathe computer 20, the animal table of the information of the latticeanimal stored in the form of the table, and the coordinate data of thepolygon indicating the schematic position of the pattern edge.

[0283] The computer 20 in the present embodiment controls the wholeapparatus and extracts the recipe file, the image data of the pattern,and the data of the lattice animal from the memory 24 to execute theabove-described image processing, the extraction of the pattern contour,and the searching of the pattern edge. The computer 20 in the presentembodiment is connected to the electronic optical system 12 of theapparatus 10 via the electronic optical system controller 22 to supplythe control signal to the electronic optical system controller 22 and toscan the electron beam EB on the upper surface of the substrate W. Whenthe scanning method of the probe in the eleventh embodiment is executed,the control signal includes a scanning signal generated based on thecoordinate data of the edge searching direction calculated from thecomplex or electrostatic potential.

[0284] The display 26 is connected to the computer 20 to display theimage to be inspected and reference image and further to appropriatelydisplay these processing situations.

[0285] The input 28 includes a keyboard 28 a and mouse 28 b, and isconnected to the computer 20 to supply various input signals by anoperator's operation.

(13) Thirteenth Embodiment

[0286] When a semiconductor device is manufactured using at least one ofthe image processing method, the extracting method of a pattern contour,and the scanning method of a probe in the above-described first toeleventh embodiments, the fine pattern can more exactly and quickly beevaluated. As a result, it is possible to manufacture the semiconductordevice with a higher yield and for a short turn around time (TAT).

(14) Fourteenth Embodiment

[0287] A series of procedures in the extracting method of a patterncontour, the image processing method, the searching method of a patternedge, and the scanning method of a probe described in the first toeleventh embodiments may also be incorporated in the program, and readand executed by a computer which can process the image data.Accordingly, the series of procedures in the extracting method of apattern contour, the image processing method, the searching method of apattern edge, and the scanning method of a probe according to thepresent invention can be realized using a general-purpose computer whichcan process the image. The series of procedures of the extracting methodof a pattern contour, the image processing method, the searching methodof a pattern edge, and the scanning method of a probe according to thepresent invention may also be stored as the program to be executed by acomputer in recording media such as a flexible disk and a CD-ROM, andread and executed by the computer. The recording media are not limitedto portable media such as a magnetic disk and optical disk, and fixedtype recording media such as a hard disk drive and memory may also beused. The program incorporating the series of procedures of theextracting method of a pattern contour, the image processing method, thesearching method of a pattern edge, and the scanning method of a probemay also be distributed via communication (including radiocommunication) lines such as the Internet. Furthermore, the programincorporating the series of procedures of the extracting method of apattern contour, the image processing method, the searching method of apattern edge, and the scanning method of a probe may also be encrypted,modulated, or compressed, and distributed via wire communication linessuch as the internet or radio communication lines.

[0288] The embodiments of the present invention have been describedabove, but the present invention is not limited to the embodiments, andcan appropriately be modified or altered without departing from thescope and spirit thereof.

What is claimed is:
 1. An extracting method of a pattern contour,comprising: acquiring an image of a pattern to be inspected; calculatinga schematic edge position of the pattern from the image; preparing anapproximate polygon by approximating a polygon consisting of edgeshaving predetermined direction components to a contour shape of thepattern on the basis of the calculated edge position; dividing theapproximate polygon into star-shaped polygons; calculating the positionof a kernel of the star-shaped polygon; and searching an edge of thepattern in a direction connecting the kernel to an arbitrary pointpositioned on the edge of the approximate polygon.
 2. The extractingmethod of the pattern contour according to claim 1, wherein thepredetermined direction component is a direction forming an angleinteger times as much as 0° to 45° with respect to a reference directionwhich can arbitrarily be set in the image.
 3. The extracting method ofthe pattern contour according to claim 1, wherein said preparing theapproximate polygon includes: generating a lattice in the image, a unitcell of the lattice having a size larger than that of a pixel of theimage and a weight coefficient being allocated to an edge of thelattice; and applying a lattice animal onto the lattice based on theweight coefficient.
 4. The extracting method of the pattern contouraccording to claim 3, wherein said preparing the approximate polygonincludes: preparing a Voronoi diagram with respect to a vertex of thelattice animal, Voronoi regions being divided by Voronoi edges of theprepared Voronoi diagram; and synthesizing Voronoi regions which belongto the same lattice animal, and wherein; searching the edge of thepattern including setting a boundary of the synthesized Voronoi regionas that of the edge searching.
 5. The extracting method of the patterncontour according to claim 1, wherein said dividing into the star-shapedpolygons includes: dividing the approximate polygon into triangles bydrawing diagonal lines which do not intersect with one another withinthe approximate polygon; imparting three different pieces of labelinformation to all the vertices of the triangles obtained by saiddividing; and selecting one arbitrary piece of the label information tomutually synthesize the triangles sharing the vertex to which theselected label information is given.
 6. An extracting method of apattern contour, comprising: acquiring an image of a pattern to beinspected; calculating a schematic edge position of the pattern from theimage; generating a lattice whose unit cell has a size larger than thatof a pixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;applying a lattice animal onto the lattice based on the weightcoefficient; and outputting contour data of the pattern based oncoordinate data of a vertex of the applied lattice animal.
 7. A programwhich allows a computer to implement an extracting method of a patterncontour, comprising: acquiring an image of a pattern to be inspected;calculating a schematic edge position of the pattern from the image;preparing an approximate polygon by approximating a polygon consistingof edges having predetermined direction components to a contour shape ofthe pattern on the basis of the calculated edge position; dividing theapproximate polygon into star-shaped polygons; calculating the positionof a kernel of the star-shaped polygon; and searching an edge of thepattern in a direction connecting the kernel to an arbitrary pointpositioned on the edge of the approximate polygon.
 8. A program whichallows a computer to implement an extracting method of a patterncontour, comprising: acquiring an image of a pattern to be inspected;calculating a schematic edge position of the pattern from the image;generating a lattice whose unit cell has a size larger than that of apixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;applying a lattice animal onto the lattice based on the weightcoefficient; and outputting contour data of the pattern based oncoordinate data of a vertex of the applied lattice animal.
 9. Amanufacturing method of a semiconductor device, comprising an extractingmethod of a pattern contour, the extracting method comprising: acquiringan image of a pattern to be inspected; calculating a schematic edgeposition of the pattern from the image; preparing an approximate polygonby approximating a polygon consisting of edges having predetermineddirection components to a contour shape of the pattern on the basis ofthe calculated edge position; dividing the approximate polygon intostar-shaped polygons; calculating the position of a kernel of thestar-shaped polygon; and searching an edge of the pattern in a directionconnecting the kernel to an arbitrary point positioned on the edge ofthe approximate polygon.
 10. A manufacturing method of a semiconductordevice, comprising an extracting method of a pattern contour, theextracting method comprising: acquiring an image of a pattern to beinspected; calculating a schematic edge position of the pattern from theimage; generating a lattice whose unit cell has a size larger than thatof a pixel of the image and to whose each edge a weight coefficient isallocated on the image on the basis of the calculated edge position;applying a lattice animal onto the lattice based on the weightcoefficient; and outputting contour data of the pattern based oncoordinate data of a vertex of the applied lattice animal.
 11. An imageprocessing method comprising: acquiring an image of a pattern to beinspected; extracting a part of a point sequence which belongs to acontour of the pattern; preparing a Voronoi diagram with respect to theextracted partial point sequence; searching a point which belongs to anedge of the pattern along an edge of the prepared Voronoi diagram toincorporate the searched point into the partial point sequence; andremoving the edge of the Voronoi diagram intersecting with the contourof the pattern to define a sub-region in the image.
 12. The imageprocessing method according to claim 11, further comprising: recursivelyrepeating said preparing the Voronoi diagram, said incorporating thesearched point into the partial point sequence, and defining thesub-region in the image, with respect to at least a part of the image.13. The image processing method according to claim 11, wherein saidextracting a part of the point sequence belonging to the contour of thepattern includes: searching the edge of the pattern along an outerperiphery of a whole region of the image or a pre-defined boundary of aregion to be inspected in the image.
 14. The image processing methodaccording to claim 11, wherein said extracting a part of the pointsequence belonging to the contour of the pattern includes: searching theedge of the pattern along a continuous line which divides a whole regionof the image or a pre-defined region to be inspected in the image intotwo regions.
 15. The image processing method according to claim 11,wherein said extracting a part of the point sequence belonging to thecontour of the pattern includes: preparing a lattice having a latticeconstant equal to a minimum linear width of the pattern included in awhole region of the image or a pre-defined region to be inspected in theimage; and searching the contour of the pattern along the preparedlattice.
 16. The image processing method according to claim 11, furthercomprising: comparing a geometric shape or connectivity of the Voronoidiagram or a part of the Voronoi diagram with that of another Voronoidiagram or a part of another Voronoi diagram to define a partial regionof the image.
 17. A program which allows a computer to implement animage processing method comprising: acquiring an image of a pattern tobe inspected; extracting a part of a point sequence which belongs to acontour of the pattern; preparing a Voronoi diagram with respect to theextracted partial point sequence; searching a point which belongs to anedge of the pattern along an edge of the prepared Voronoi diagram toincorporate the searched point into the partial point sequence; andremoving the edge of the Voronoi diagram intersecting with the contourof the pattern to define a sub-region in the image.
 18. A manufacturingmethod of a semiconductor device, comprising an image processing methodincluding: acquiring an image of a pattern to be inspected; extracting apart of a point sequence which belongs to a contour of the pattern;preparing a Voronoi diagram with respect to the extracted partial pointsequence; searching a point which belongs to an edge of the patternalong an edge of the prepared Voronoi diagram to incorporate thesearched point into the partial point sequence; and removing the edge ofthe Voronoi diagram intersecting with the contour of the pattern todefine a sub-region in the image.
 19. A searching method of a patternedge, comprising: acquiring an image of a pattern to be inspected anddata of a line representing a schematic edge position of the pattern;defining one arbitrary point in the image as a start point of edgesearching, and defining at least one point on the line as a point in anedge searching direction; and searching the edge of the pattern from thestart point of the edge searching and along at least one curve of acurve group given by either a real part or an imaginary part of aholomorphic function, a trajectory of said curve passing through thepoint in the edge searching direction.
 20. The searching method of thepattern edge according to claim 19, wherein said holomorphic function isanalogous to a complex potential of a two-dimensional ideal fluid systemwhich includes at least one source point and at least one sink point.21. The searching method of the pattern edge according to claim 20,wherein said holomorphic function is analogous to a complex potential ofa two-dimensional ideal fluid system in which the source point isdisposed adjacent onto a finite line segment or in which the sink pointis disposed adjacent onto the finite line segment or in which the sourcepoint and the sink point have a relation of a mirror image with eachother with respect to the line representing the schematic edge position.22. The searching method of the pattern edge according to claim 19,wherein said holomorphic function is analogous to a complex potential ofa two-dimensional electromagnetism system which includes at least onepositive point charge and at least one negative point charge.
 23. Thesearching method of the pattern edge according to claim 22, wherein saidholomorphic function is analogous to a complex potential of atwo-dimensional electromagnetism system in which the positive pointcharge is disposed adjacent onto a finite line segment or in which thenegative point charge is disposed adjacent onto the finite line segmentor in which the positive point charge and the negative point charge havea relation of a mirror image with each other with respect to the linerepresenting the schematic edge position.
 24. The searching method ofthe pattern edge according to claim 19, wherein data of the linerepresenting the schematic edge position is obtained based on layoutdata included in design data of the pattern.
 25. A program which allowsa computer to implement a searching method of a pattern edge, saidsearching method comprising: acquiring an image of a pattern to beinspected and data of a line representing a schematic edge position ofthe pattern; defining one arbitrary point in the image as a start pointof edge searching, and defining at least one point on the line as apoint in an edge searching direction; and searching the edge of thepattern from the start point of the edge searching and along at leastone curve of a curve group given by either a real part or an imaginarypart of a holomorphic function, a trajectory of said curve passingthrough the point in the edge searching direction.
 26. A manufacturingmethod of a semiconductor device, comprising a searching method of apattern edge, said searching method including: acquiring an image of apattern to be inspected and data of a line representing a schematic edgeposition of the pattern; defining one arbitrary point in the image as astart point of edge searching, and defining at least one point on theline as a point in an edge searching direction; and searching the edgeof the pattern from the start point of the edge searching and along atleast one curve of a curve group given by either a real part or animaginary part of a holomorphic function, a trajectory of said curvepassing through the point in the edge searching direction.
 27. A methodof scanning a probe onto at least a part of an observation regionincluding a pattern to be inspected, comprising: defining one arbitrarypoint in the observation region as a start point of probe scanning, anddefining at least one point on a line representing the schematic edgeposition of the pattern as a point in a probe scanning direction; andscanning the probe from the start point of the probe scanning and alongat least one curve of a curve group given by either a real part or animaginary part of a holomorphic function, a trajectory of the scanningpasses through a point in the probe scanning direction.
 28. The scanningmethod of the probe according to claim 27, wherein said holomorphicfunction is analogous to a complex potential of a two-dimensional idealfluid system which includes at least one source point and at least onesink point.
 29. The scanning method of the probe according to claim 28,wherein said holomorphic function is analogous to a complex potential ofa two-dimensional ideal fluid system in which the source point isdisposed adjacent onto a finite line segment or in which the sink pointis disposed adjacent onto the finite line segment or in which the sourcepoint and the sink point have a relation of a mirror image with eachother with respect to the line representing the schematic edge position.30. The scanning method of the probe according to claim 27, wherein saidholomorphic function is analogous to a complex potential of atwo-dimensional electromagnetism system which includes at least onepositive point charge and at least one negative point charge.
 31. Thescanning method of the probe according to claim 30, wherein saidholomorphic function is analogous to a complex potential of atwo-dimensional electromagnetism system in which the positive pointcharge is disposed adjacent onto a finite line segment or in which thenegative point charge is disposed adjacent onto the finite line segmentor in which the positive point charge and the negative point charge havea relation of a mirror image with each other with respect to the linerepresenting the schematic edge position.
 32. A program to allow acomputer to implement a method of scanning a probe onto a sample havingan observation region, the computer controlling an inspection apparatusto generate the probe and to scan the probe onto at least a part of theobservation region in which the pattern to be inspected is formed, thescanning method comprising: defining one arbitrary point in theobservation region as a start point of probe scanning, and defining atleast one point on a line representing a schematic edge position of thepattern as a point in a probe scanning direction; and scanning the probefrom the start point of the probe scanning and along at least one curveof a curve group given by either a real part or an imaginary part of aholomorphic function, a trajectory of the scanning passes through apoint in the probe scanning direction.
 33. A manufacturing method of asemiconductor device, comprising a method of scanning a probe onto atleast a part of an observation region in which a pattern to be inspectedis formed, said method of scanning the probe including: defining onearbitrary point in the observation region as a start point of probescanning, and defining at least one point on a line representing aschematic edge position of the pattern as a point in a probe scanningdirection; and scanning the probe from the start point of the probescanning and along at least one curve of-a curve group given by either areal part or an imaginary part of a holomorphic function, a trajectoryof the scanning passes through a point in the probe scanning direction.34. A pattern inspection apparatus comprising: a first calculator whichreceives data of an image of a pattern to be inspected and calculates aschematic edge position of the pattern from the image; an imageprocessor which approximates a polygon constituted of edges exclusivelyhaving predetermined direction components to a contour shape of thepattern based on the calculated edge position to prepare an approximatepolygon and which divides the approximate polygon into star-shapedpolygons; a second calculator which calculates a position of a kernel ofthe star-shaped polygon; and an edge searcher which searches an edge ofthe pattern in a direction connecting the kernel to an arbitrary pointpositioned on an edge of the approximate polygon.
 35. A patterninspection apparatus comprising: a calculator which receives data of animage of a pattern to be inspected and calculates a schematic edgeposition of the pattern from the image; an image processor whichgenerates a lattice on the image based on the calculated edge position,a unit cell of the lattice having a size larger than that of a pixel ofthe image and a weight coefficient being allocated to each edge of thelattice, said image processor applying a lattice animal onto the latticebased on the weight coefficient; and an edge searcher which outputscontour data of the pattern based on coordinate data of a vertex of theapplied lattice animal.
 36. A pattern inspection apparatus comprising: apoint sequence extractor which receives data of an image of a pattern tobe inspected and which extracts a part of a point sequence belonging toa contour of the pattern; an image processor which prepares a Voronoidiagram with respect to the extracted partial point sequence and whichsearches a point belonging to the edge of the pattern along an edge ofthe prepared Voronoi diagram to incorporate the searched point into thepartial point sequence and which removes an edge of the Voronoi diagramintersecting with the contour of the pattern to define a sub-region inthe image; and an edge searcher which searches the edge of the patternfor each sub-region.
 37. A pattern inspection apparatus comprising: asetter which receives data of an image of a pattern to be inspected anddata of a line representing a schematic edge position of the pattern toset a start point of edge searching and at least one point on the lineas the point in an edge searching direction in the image; a calculatorto calculate a curve group which is given by either a real part or animaginary part of a holomorphic function and each of which passesthrough the point in the edge searching direction from the start point;and an edge searcher which searches an edge of the pattern along atleast one cure in the curve group.
 38. A pattern inspection apparatusconnectable to a probe scanning device scanning a probe onto a sample inwhich a pattern to be inspected is formed, the pattern inspectionapparatus comprising: a calculator which receives image data of thepattern and data of a line representing a schematic edge position of thepattern to calculate a curve group given by either a real part or animaginary part of a holomorphic function and passing through at leastone point on the line representing the schematic edge position from thestart point; and a controller which generates a control signal to scanthe probe along at least one curve in the curve group and which suppliesthe control signal to the probe scanning device.